Calculating Volume by Rotating y = e^x * sin(x) Around the x-Axis

[TSN79]

I'm supposed to find the volume of the figure that appears by rotating the follwing around the x-axis:
$$y = e^x \cdot \sin (x) & x \in \left[ {0,\left. \pi \right]} \right.$$
This means (I think) that the function needs to be to the second power and multiplied by Pi in an integral. So the integral becomes
$$\pi \int {e^{2x} \cdot \sin ^2 (x)dx}$$
I need hints on how to solve this integral, I've tried integration by parts but not really gotten anywhere...am I on the right track?

 

[1800bigk]

here is a hint, maybe change sin squared into something more friendly.

 

[TSN79]

I tried to change it into 1-cos2x = 2(sinx)^2, but I didn't find it to make it any easier...was that what you thought about?

 

[1800bigk]

yes, change (sinx)^2 = 1/2 - (1/2)cos2x. multiply your e function through and you will have 2 integrals that can be solved. the integral with (e^2x)(1/2 cos 2x) is going to need parts twice.

 

[TSN79]

I do believe you might be on to something there 1800bigk...thx!